Most people sound like better singers inside their own heads than they do to others. This is mostly because the perception of a voice sounding rich has a lot to do with the presence of high harmonics above the fundamental frequency of the note – pretty much the same reason why a banjo sounds different to a clarinet, which sounds different to a steel drum, even if they’re all playing the same note.

Unfortunately, it turns out that having to travel through the air en route to a listener’s eardrum is bad news for these harmonics. They travel much better (i.e. are attenuated less) through other media, such as bone. Hence why people sound better in their own heads – a lot of the sound waves they’re picking up went through their body, not through the air. While practising this morning I found a way to increase this effect, and thus instantly become a better singer. The catch is that nobody else will notice. 🙂

Take both hands and use your index and middle fingers to push back your ears, gently but firmly, until they touch your head. Let your palms rest about an inch from your cheeks. Sound better? This helps in a few ways. Sound travelling down your arms is redirected to your ears, where it is needed. Another is that your ears can pick up extra vibrations from your head. Finally, sound exiting your mouth is picked up by your hands and reflected through the air, as well as travelling up your arms to your ears. After some preliminary experimentation using different positions and so on, I think the most important factor is the palms.

To demonstrate my suspicion that probability and statistics are far more interesting in their foundations than in their practice, here’s a quote from Cambridge philosopher Arif Ahmed:

“The only source of empirical evidence we have for assigning one likelihood rather than another is repeated trials. If I have a die, and it’s got six sides, we might say it’s got a chance of one sixth of coming out with a six. But supposing you roll it 20 times and it comes up six every time, you’ll think it’s probably loaded. You can’t simply establish these probabilities a priori.” (28/04/2005)

Ahmed teaches a course called “Sets, Relations and Probability”, so his views are certainly not naive. (Brendon would have noticed his use of the word “likelihood”, and suspected the presence of a meta-expert). I contend that they are, however, wrong.

Let the comments begin! I’ll make my views known as the discussion continues, and I might produce a summarising post in a few weeks.

My physics education, like everyone’s, has a few weak points. One of those weak points for me was general relativity. My introduction to it was in an honours mathematics course, which started easily enough with some familiar special relativity, until about the 4th lecture. This particular lecture proceeded as follows:

I dropped out of the course after the next lecture, but rejoined it towards the end (ahh, the freedom of graduate level courses). By then it had moved on to things like finding geodesics of a particular spacetime and using those to work out classical predictions such as the perihelion shift of Mercury and the deflection angle of light as it passes the sun, the topic of Eddington’s famous 1919 observations. I could handle this part, which is why I returned to the course. Anyhow, I ended up getting quite a good mark thanks to a reasonably straightforward exam and generous School of Physics scaling. But I felt that I didn’t really understand general relativity much at all.

This changed after spending three and a half years sharing an office with cosmologists (such as the co-authors of the blog) and listening in (and interjecting inappropriately) to their discussions. Soon, I found myself able to predict their responses to my questions. I recently realised that this latter ability means that I actually do, at some level, understand general relativity – just don’t ask me to do any actual calculations. Am I a meta-expert in general relativity because my brain contains a model that accurately predicts the comments of real experts? Perhaps a more realistic term would be pseudo-expert.

Perhaps, or maybe I’m being over-optimistic. I regard myself as a genuine expert on Bayesian Inference, and many of my colleagues have become meta-experts after listening to my ramblings on this topic. However there are occasional hints of flaws in their model, such as the word “likelihood” used in the wrong context. I’m sure I’ve said a few GR howlers from time to time, such as my apparently flawed (but I’m yet to understand why) understanding that someone falling into a Schwarzschild black hole has a reasonable chance of being saved due to time dilation (to an observer at infinity, the person never actually crosses the event horizon, and therefore can always be rescued).

I’d be interested to hear about your experiences with the phenomenon of meta-expertise.